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Independent and Dependent Events/Transcript
Transcript Title text reads: The Mysteries of Life with Tim and Moby. A penny flips through the air and lands in his hand. Tim flips the penny into the air again as Moby beeps. Tim catches the coin. TIM: Nope, heads. On-screen, Tim flips the coin again. Moby beeps. TIM: Sorry, heads again. On-screen, Tim flips the coin again. Moby beeps. TIM: Oh, no, sorry. The answer was tails. Tails. Moby beeps and looks skeptical. A letter appears. Text reads as Tim narrates: Dear Tim and Moby, If there's a 50 percent chance of rain on Saturday and a 25 percent chance of rain on Sunday, does that mean there’s a 75 percent chance that it will rain all weekend? From, Jocelyn TIM: Uhmm, no. This question involves probability: how likely some event is going to happen. In this case, you have 2 single events: the weather on Saturday and the weather on Sunday. On-screen, a calendar appears, with Saturday and Sunday highlighted. TIM: Okay, on Saturday, there's a 50 percent chance of rain. 50 percent is equal to one-half, so there’s a 1 in 2 probability that it'll rain that day. On-screen, an image of a raincloud appears on the calendar for Saturday. Text reads, 50 percent. The fraction, one-half, also appears. TIM: And for Sunday, the forecast is predicting a 25 percent chance of rain. 25 percent is the same as saying one-fourth, so that's a 1 in 4 chance of rain for Sunday. On-screen, an image of a raincloud appears on the calendar for Sunday. Text reads, 25 percent. The fraction, one-fourth, also appears. TIM: The probability of it raining on Saturday has no effect on the probability of it raining on Sunday. They're independent events. A label appears, reading, independent events. TIM: To find the probability of both independent events happening, we multiply the probability of the first event by the probability of the second event. So, the probability of rain on Saturday, one-half, times the probability of rain on Sunday, one-fourth, is equal to one-eighth, or 12.5 percent. An equation appears, reading, one-half, times one-fourth, equals one-eighth, which equals 12.5 percent. TIM: There's a 12.5 percent chance that it will rain on both Saturday and Sunday. Moby beeps. TIM: Well, dependent events happen when the outcome of one event has an effect on the outcome of another. A label appears, reading, dependent events. TIM: Say we've got three paper bags. Two of the bags each contain an apple, and one contains a dirty golf ball. On-screen, three paper bags appear. Their contents are revealed. Each of the first two bags contains an apple, while the third bag contains a dirty golf ball. Tim takes the first bag. TIM: The probability of me ending up with an apple is two-thirds; that's two apples out of three bags. An equation appears, reading, apple equals two-thirds. Tim looks in his bag. TIM: Whaddaya know? I got an apple. We know that one of those remaining bags has a dirty golf ball in it, and the other has an apple in it. On-screen, there are two bags left. It's revealed that the first bag contains an apple, while the second contains the dirty golf ball. Moby’s hand hovers over the bags. TIM: The probability that Moby gets an apple is one-half: one apple, two bags. An equation appears, reading, apple equals one-half. Moby picks up the second bag, looks inside it, and beeps. TIM: Did you get the apple? Moby holds up the dirty golf ball. He looks angry. TIM: Anyway, choosing those bags are dependent events; my choice affected the probability of Moby getting an apple. Moby beeps. TIM: How likely was it that we'd both choose apples? Well to calculate that, we take the probability of me choosing an apple, two-thirds, and multiply it by the probability of Moby choosing an apple, or one-half. Moby looks at his dirty golf ball. A formula reads, two-thirds times one-half. TIM: two-thirds times one-half equals two-sixths, which reduces to one-third. An equation appears, reading, two-thirds times one-half equals two-sixths, which equals one-third. TIM: So, there was a 33.3 percent chance that Moby and I would both get apples. On-screen, an equation reads, one-third equals 33.3 percent. TIM: That makes sense when you think about it because one-half, or 50 percent, of two-thirds is equal to one-third, or 33.3 percent! On-screen, a pie chart appears, with three equally sized wedges. At first, two of the wedges are green. Then, only one wedge is green, representing 33.3 percent of the pie. The number, 33.3 percent, appears. Moby beeps and holds up his golf ball. TIM: I don't wanna trade. Just take the other bag! Moby beeps and offers Tim his dirty golf ball again. TIM: No, this is my apple. I'm not trying to trick you. Moby beeps. TIM: Take the bag, you've got a 100 percent chance of getting an apple! Moby extends his arm to reach for Tim's apple. TIM: Aaah! Cut it out! Category:BrainPOP Transcripts